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Byju's Answer
Standard IX
Mathematics
Parallelograms on the Same Base and between the Same Parallels
𝔸
Question
In the figure given above, the ratio
A
r
e
a
o
f
D
P
Q
C
A
r
e
a
o
f
A
B
C
D
=____.
A
1
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B
1
2
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C
2
3
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D
1
3
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Solution
The correct option is
C
2
3
Let h be the height between the parallel lines AB and CD
P
Q
=
1
3
A
B
Hence, area of DPQC =
1
2
×
h
t
i
m
e
s
(
P
Q
+
D
C
)
=
h
2
×
(
D
C
+
A
B
3
)
=
h
2
×
(
D
C
+
D
C
3
)
=
h
2
×
(
4
D
C
3
)
=
2
h
×
D
C
3
Now, we know that
h
×
D
C
=
area of parallelogram ABCD
Hence, area of trapezium DPQC =
2
3
×
area of parallelogram ABCD
Thus,
A
r
e
a
o
f
D
P
Q
C
A
r
e
a
o
f
A
B
C
D
=
2
3
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Q.
In the given figure, ABP is a straight line and BD||PC.Area
Δ
A
P
D
=
___
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Standard IX Mathematics
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